In article ,
Nicolaas Vroom writes:

We know that the universe is approximately flat. Assuming a simple
topology, that means that it is either infinite or very much larger
than the particle horizon (the theoretical limit of how far we can
see; in practice that limit is essentially the last scattering surface
[which is operationally defined as the surface at which the universe
becomes optically thick]). So, essentially all astronomers in the
world agree that there are more galaxies than we can see, even more
than we could see with arbitrarily powerful instruments.

I do not fully agree with your argumentation.

Why not?

When you want to understand what we can observe you have to use the
friedmann equations.
To see the results select:
http://users.telenet.be/nicvroom/friedmann's%20equation%20L=0.01155.htm
In Figure 1B it is the blue line what we can see/observe.
The black line is the maximum distance of the Universe as the result
of the Big Bang. I expect this is the particle/radiation limit.
At present the size of the Universe is roughly 35 bly.

OK. How does that contradict my text above?

Note: The OBSERVABLE universe can be arbitrarily smaller than the ENTIRE
universe.

From this simulation the claim that the expansion of the universe
undergoes acceleration is arbitrary.

Not sure what you mean by "arbitrary". Based on the observed values of
the parameters, the universe is accelerating now and will do so forever,
asymptotically approaching the de Sitter model with exponential
expansion.

This also means that if you have a more powerfull instrument
you can not see more galaxies but only the same galaxies (in the past)
more accurate.

With a more powerful instrument, one cas see galaxies fainter than the
lower limit of a less powerful instrument. Of course, if there is some
faintest galaxy, then once that is observable a better instrument won't
show more galaxies.